The shape of the cavity is determined by measuring the near-field data of the curve or surface inside the cavity. The inverse scattering problem of a fully coated penetrable cavity with interior measurements is studied by the factorization method. First, the mathematical model of the inverse scattering problem is presented in the form of radiation scattering field. Next, the decomposition of the cavity near-field data operator is studied by constructing the principal factorization of the operator under the condition of full coating, Finally, assuming that the constructed operator satisfies the appropriate conditions, the range of the data operator is found and the shape of the cavity is described.